2 Scientific Notation Section 2.1 Objective: show how very large or very small numbers can be expressed as the product of a number between 1 and 10 AND a power of 10
3 (the number of atoms in a drop of water) Scientific NumbersIn science, we often encounter very large and verysmall numbers. Using scientific numbers makesworking with these numbers easier5,010,000,000,000,000,000,000a very large number(the number of atoms in a drop of water)a very small number(mass of a gold atom in grams)
4 Scientific NumbersRULE 1As the decimal is moved to the leftThe power of 10 increases onevalue for each decimal place movedAny number to theZero power = 1450,000,000 = 450,000,000. x 108231450,000,000 = 450,000,000. x 1084.5 x 10
5 Scientific Numbers 0.0000072 = 0.0000072 x 10 -6 -2 -3 -1 RULE 2As the decimal is moved to the rightThe power of 10 decreases onevalue for each decimal place movedAny number to theZero power = 1= x 10-6-2-3-1= x 10-67.2 x 10
6 UNITS and MEASUREMENTS OF LENGTH, VOLUME & MASS Section 2.2 and 2.3UNITS and MEASUREMENTS OF LENGTH, VOLUME & MASSObjective: to learn english, metric and SI systems of measurement
7 Measurements of length, volume & mass Section 2.3Measurements of length, volume & massObjective: understand metric system for measuring length, volume and mass
8 Property English Unit Metric Unit Fundamental QuantitiesProperty English Unit Metric Unitmass slug gram1.0 slug ,590 glength foot meter1.0 ft mvolume quart liter1.06 qt L
9 Property Metric Unit English Unit time second secondtemperature Kelvin Fahrenheit
10 Significant Figures Section 2.5 Objective: to learn how to determine the number of sig figs
11 Significant Figures All number other then zero are significant Ex. 23 = 2 sig figsLeading zeros- zeros that are at the beginning of a number are NEVER significantEx 034 = 2 sig figs and = 3 sig figsTrapped zeros – zeros that are trapped between two other significant figures are ALWAYS significantEx 304 = 3 sig figs and = 5 sig figsTrailing zeros – zeros that are at the end of a number – depends on if there is a decimal point expressed in that numberIf there is a decimal point showing in the number then the zeros are significantEx 60 = 1 si fig but 60. = 2 sig figs and 60.0 = 3 sig figsEx .05 = 1 sig figsIf there is NOT a decimal point showing in the number then the zeros are NOT sinificant
13 Significant Figures 120000 120000. No decimal point Zeros are not 2 sig figsZeros are notsignificant!DecimalPointAll digits includingzeros to the left ofThe decimal aresignificant.6 sig figs
14 Significant Figures 1005 123.00 All figures are Significant 4 sig figs Zeros betweenNon zeros aresignificant123.00All figures areSignificant5 sig figsZero to theRight of theDecimal aresignificant
15 Zeros to the right of the decimal And to the right of non zero values Significant Figures3 sig figsZeros to the right ofThe decimal with noNon zero valuesBefore the decimalAre not significant5 sig figsZeros to the right of the decimalAnd to the right of non zero valuesAre significant
16 Significant Figures 1 in = 2.54cm 4 quarts = 1 gallon Exact equivalences have an unlimited number ofsignificant figures1 in = 2.54cmTherefore in the statement 1 in = 2.54 cm,Neither the 1 nor the 2.54 limits the number ofSig figs when used in a calculationThe same is true for:4 quarts = 1 gallon100 centimeters = 1 meter1000 grams = 1 kilogramsand so on !
17 (numbers that were not obtained using measuring Exact numbers(numbers that were not obtained using measuringdevices, but determined by counting)also have an unlimited number of sig figsExamples:3 apples8 molecules32 students
18 Uncertainty in Measurement Section 2.4Uncertainty in MeasurementObjective: to understand how uncertainty in measurement arisesDifference between accuracy and precision
19 Significant FiguresSignificant figures are used to distinguish truly measured values from those simply resulting from calculation. Significant figures determine the precision of a measurement. Precision refers to the degree of subdivision of a measurement.As an example, suppose we were to ask you to measure how tall the school is, you replied “About one hundred meters”. This would be written as 100 with no decimal point included. This is shown with one significant figure the “1”, the zeros don’t count and it tells us that the building is about 100 meters but it could be 95 m or even 104 m. If we continued to inquire and ask you to be more precise, you might re-measure and say “ OK, ninety seven meters. This would be written as 97m. It contains two significant figures, the 9 and the 7. Now we know that you have somewhere between 96.5m and 97.4m. If we continue to ask you to measure even more precise with more precision, may eventually say, “97.2 m”.THE PRECISION OF YOUR MEASUREMENT IS DICTATED BY THE INSTRUMENT YOU ARE USING TO MEASURE!!!!
20 Precision = Accuracy ACCURACY MEANS HOW CLOSE A MEASUREMENT IS TO THE TRUE VALUEPRECISION REFERS TO THE DEGREE OFSUBBDIVISION OF THE MEASUREMENTFOR EXAMPLE, IF A ROOM IS 10 FEET LONG ANDYOU MEASURE IT TO BE FT LONG, YOURMEASUREMENT IS VERY PRECISE BUT INACCURATE !MEASUREMENTS SHOULD BE ACCURATE AND ASPRECISE AS THE MEASURING DEVICE ALLOWS
23 Precision & Measurement Measurements are always all measured values plus oneapproximated value. The pencil is 3.6 cm long.With more calibration a moreprecise measurement is possibleThe pencil is 3.64 cm long!4The calibration of the instrumentdetermines measurement precisionNow cm !
24 What is the precision on a ruler? Follow directions from Mrs McGrath & try to figure it out???What if your measurement was in cm?What if your measurement was in mm?
25 Scales and sig figs In our class Write down what the scale says Most scales are taken to the hundreths place
26 Graduated Cylinders & Thermometers First – figure out scaleThen – take measurement out to one guess past certainity
28 Rules for rounding off In calculations: Round each number to one sig fig:If the digit is to be removed:Is less than 5, the preceding digit stays the sameEX rounds to ???? _____________is equal to or greater then 5, the preceding digit is increasedEX rounds to ???? _____________In calculations:carry the extra digits through to the final result AND THEN round off
29 Addition/Subtraction with Sig Figs Adding and subtracting with significant figures.The position, not the number, of the significant figures is important in adding and subtracting. For example,(the last sig fig is in hundredth place (0.01))(the last sig fig is in ten thousandth (0.0001))(the answer is rounded off tothe least significant positionhundredths place)
30 The answer is rounded to the position of least significance Adding & Subtracting Sig FigsThe numbers inthese positions arenot zeros, they areunknown123.6_Don’t even look atThe 6 to determineRounding. OnlyLook at the 4165.9The answer is rounded to theposition of least significance
31 Multiplying/Dividing with Significant Figures The result of multiplication or division can have no more sig figs than the term with the least number.*ex. 9 x 2 = 20 since the 9 has one sig fig and the 2 has one sig fig, the answer 20 must have only one and is written without a decimal to show that fact.* By contrast, 9.0 x 2.0 = 18 each term has two sig figs and the answer must also have two.*4.56 x 1.4 = How many sig figs can this answer have?6.4 (2 sig figs)
32 Dimensional analysis Section 2.6 Objective: learn how to apply dimensional analysis to solve problems
33 NO KING HENRYYou must use dimensional analysis to convert from metric to metricYou must use your brain and logic to do thisK H D b d c m
34 Some Common Metric Prefixes Prefix Multiplier Examplemilli millilitercenti centimeterdeci decigramkilo kilometermicro microgram6Mega megabyte9Giga gigabyte
35 From the last slide we learned the meaning of some of the common prefixes, BUT we are going to learn to dimensional analysis using the root prefixes and deciding bigger/smaller.
36 Some Common Metric Prefixes Prefix Multiplier Prefixmilli millicenti centideci decikilo kilomicro micro6Mega mega9Giga giga
37 Conversions YOU Need to Memorize Length1in = 2.54 cm39.37 in = 1 meter1 mile = 5280 feetMass1kg = 2.2 lbs1lb = 454 gramsVolume1 liter = 1.06qts1 gallon = 3.79 liters
38 Dimensional Analysis Rules 1.37days = ? minutesAlways start with the known value over the number 1Always write one number over the otherAlways, Always, Always, Always, Always write/include the unit with the number1.37 days1
39 Single step examples Equivalence statements 3.6 m = ? ft 6.07 lb = ?kg 4.2 L = ?qt35.92 cm = ? inLength1in = 2.54 cm39.37 in = 1 meter1 mile = 5280 feetMass1kg = 2.2 lbs1lb = 454 gramsVolume1 liter = 1.06qts1 gallon = 3.79 liters
40 Double step Exampls Equivalence Statements 56,345 s = ? yrs 98.3 in = ?m3.2 mi = ?kmLength1m = yd2.54 cm = 1 in1mi = 1760 ydMass1kg = lb453.6 g = 1lbVolume1 L = 1.06qt
41 Temperature Conversions Section 2.7Temperature ConversionsObjective: to learn three temperature scalesto convert from one scale to another
42 Temperature – the average kinetic energy in a substance Boiling pointsFahrenheit 212 FCelsius 100 CKelvin 373 KFreezing pointsFahrenheit 32 FCelsius 0 CKelvin K*O Kelvin or Absolute zero: point at which molecular motion stops
43 Temperature Conversion Formulas Celsius to Kelvin TK = TC + 273Kelvin to Celsius TC = TK – 273Celsius to TF = 1.80TCFahrenheitFahrenheit to TC = TF - 32Celsius
44 Section 2.8DensityObjective: to define density and its units
45 Density: the amount of matter present in a given volume of a substance UnitsFormulaDensity = g/ml OR g/cm3Mass = g (grams)Volume = ml OR cm3Liquids OR solidsDensity = mass/volumeDENSITY of a substance never changesEx gold is ALWAYS 19.3g/cm3Less dense objects “FLOAT” in more dense objects
46 Example calculationMercury has a density of 13.6g/ml. What volume of mercury must be taken to obtain 225 grams of the metal?
47 Example calculation: ANSWER Mercury has a density of 13.6g/ml. What volume of mercury must be taken to obtain 225 grams of the metal?16.5 mL